California and four other states may put initiatives on the ballot in November. A recent poll shows a clear majority of Americans supports legalizing pot.

SEATTLE — The new year is shaping up to be one of the marijuana movement’s strongest ever.

The first legal pot storefronts in America opened to long lines in Colorado 20 days ago. Washington state is poised to issue licenses for producing, processing and selling the Schedule I drug — once officials sift through about 7,000 applications.

Signature gatherers have been at work in at least five states, including California, to put marijuana measures on the ballot in 2014. On Wednesday, organizers announced they had gathered more than 1 million signatures in favor of putting a medical marijuana measure before voters in Florida, a high-population bellwether that could become the first Southern state to embrace pot.

“Florida looks like the country as a whole,” said Ben Pollara, campaign manager for the Sunshine State’s effort. “If Florida does this, it is a big deal for medical marijuana across the country.”

Just three months ago, a clear majority of Americans for the first time said the drug should be legalized — 58% of those surveyed, which represents a 10-percentage-point jump in just one year, according to Gallup. Such acceptance is almost five times what Gallup found when public opinion polling on marijuana began in 1969.

And last month in California, where the legalization measure Proposition 19 went down to defeat in 2010, the Field Poll reported what it called its first clear majority in favor of legalizing pot — 55% of those polled, compared with 13% in 1969.

“What has happened now is we have reached the national tipping point on marijuana reform,” said Stephen Gutwillig, deputy executive director of the Drug Policy Alliance, an advocacy group. “Marijuana legalization has gone from an abstract concept to a mainstream issue to a political reality within a three-year period.”

The Obama administration said last year it would not interfere in states that allowed commercial marijuana sales — as long as they were strictly regulated. But pot remains illegal under federal law, and messages from on high are mixed.

On Wednesday, the chief of operations for the Drug Enforcement Administration, James L. Capra, told a Senate panel, “Going down the path to legalization in this country is reckless and irresponsible.”

But in a lengthy New Yorker interview published Sunday, President Obama said of legalization in Washington and Colorado: “It’s important for it to go forward because it’s important for society not to have a situation in which a large portion of people have at one time or another broken the law and only a select few get punished.”

Obama said of marijuana, “I don’t think it is more dangerous than alcohol.”

The big question, of course, is why attitudes toward marijuana are shifting now. And the answer, according to pollsters and drug policy experts, is a complicated stew of demographics, personal experience, electoral success and the failure of existing drug policy.

To Alison Holcomb, the American Civil Liberties Union attorney who wrote the ballot measure that legalized recreational marijuana in Washington state, the “enormous jump” in approval of legalization in just a year does not reflect “changes in attitudes about marijuana specifically. Rather, it’s a change in attitudes about whether it’s OK to support marijuana law reform.”

In other words, Americans don’t necessarily like pot more than they used to. The percentage of those who have actually tried it has stayed in the 30% range for three decades. Rather, Americans are simply fed up with criminal penalties they say are neither cost-effective nor just.

Those looking for evidence of marijuana’s momentum need look only to Jan. 8.

That’s the day recreational pot supporters delivered about 46,000 signatures to election officials in Alaska — 50% more than required — putting a measure on legalization one step closer to a vote in the largely Republican state.

That same afternoon in deeply Democratic New York, Gov. Andrew Cuomo, a former prosecutor with a history of opposing the drug, announced a modest medical marijuana pilot project.

“Research suggests that medical marijuana can help manage the pain and treatment of cancer and other serious illnesses,” an uncomfortable looking Cuomo said, giving the subject 27 seconds in a nearly 90-minute State of the State address.

As Cuomo noted, an increasing number of states have enacted medical marijuana laws. California was the first in 1996, followed by 20 others and the District of Columbia.

The embrace of medical marijuana to ease ills including Alzheimer’s disease and seizures is one reason that support for marijuana has continued to grow. Just listen to the Pepper family.

The drugs that Riverside lawyer Letitia Pepper, 59, took to slow the progression of her multiple sclerosis caused side effects worse than the disease itself, with its numbness, loss of dexterity and temporary loss of vision.

The only relief, Pepper said, came when she began using marijuana in 2007. Today she is gathering signatures to get the California Cannabis Hemp Initiative 2014 on the ballot.

She had grown up, she said, as “a good girl. My homework was done. I knew marijuana was illegal.” She tried it once when she was 25, didn’t like it and left it behind. Until she needed it to help her function.

Pepper’s improvement wasn’t lost on her mother, Lorraine, 85, of Oceanside. Two years ago, the retired home economics teacher had surgery to repair a hiatal hernia; her stomach had migrated through the hole in her diaphragm into her chest cavity.

“Since that time, my brain hasn’t worked like it used to, and my body hasn’t either,” said the elder Pepper, who opposed marijuana until her daughter began using it. She takes it as well, in a nonintoxicating liquid form. “Anything that will help, I will try. I don’t think I sense a great improvement, but I have gradually gotten better.”

Although people 65 and older are the only age group that pollsters say still opposes legalization, their support for the drug has also jumped more in recent years than that of any other age group. Between 2011 and 2013, Gallup found that the percentage of older Americans in favor of legalization rose 14 percentage points — more than double any other group surveyed.

Graham Boyd, who has worked on marijuana legalization efforts nationwide, agrees that “the big movement is among older and more conservative voters.” But Boyd said internal polling showed that new converts to marijuana support “don’t particularly like marijuana, don’t have much experience in using marijuana and aren’t deeply attached to the position.”

This is not, he said, “a hooray-for-marijuana vote. It’s a vote that what we are doing now is not working.”

Boyd was counsel for the late philanthropist Peter Lewis, who commissioned a long-term, in-depth research project after the defeat of California’s Proposition 19 to understand the “landslide retreat from marijuana support.”

That effort, Boyd said, revealed that “instead of talking about the virtues of marijuana, we need to talk about the better approach of control through regulation.” Democratic pollster Anna Greenberg, who spearheaded Lewis’ research project, said that message connected with voters in Washington state and Colorado.

Once voters approved legalization in Washington and Colorado in 2012, public opinion began to change dramatically — enough so that marijuana advocates have high hopes for 2014 and 2016.

“The ice-breaking effect of Washington and Colorado allowed more people to say [legalization] might be an option,” said the ACLU’s Holcomb. “If Oregon and Alaska go [for legalization] it will be very big. … And I’m holding out hope for California. If California goes in 2014, that’s going to be huge.”